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%I #8 Feb 06 2020 06:26:19
%S 1,6,30,330,390,2730,5460,12090,60060,92820,223860,1021020,1922700,
%T 3805620,13458900,41861820,110362980,113573460,227146920,251170920,
%U 502341840,563603040,888287400,1270629360,1776574800,3310889400,23107724640,27939071160,33754921200,36419783400
%N Indices of records in A332040.
%C Numbers k such that esigma(x) = k has more solutions x than any smaller k, where esigma(x) is the sum of exponential divisors of x (A051377).
%C The exponential version of A145899.
%C The corresponding number of solutions for each term is 1, 2, 5, 6, 8, 9, 10, 12, 15, 16, 19, 22, 27, 29, 35, 37, 38, 44, 45, 47, 50, 51, 52, 53, 66, 80, 83, 89, 95, 102.
%e There are 2 solutions to esigma(x) = 6: esigma(4) = esigma(6) = 6. For all m < 6 there are no more than one solution to esigma(x) = m, thus 6 is in the sequence.
%t f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; m = 10000; v = Table[0, {m}]; Do[sig = esigma[k]; If[sig <= m, v[[sig]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
%Y Cf. A051377, A145899, A289132, A332037, A332039, A332040.
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 05 2020
%E a(26)-a(30) from _Giovanni Resta_, Feb 06 2020
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